Select The Correct Answer.The Endpoints Of $\overline{GH}$ Are $G(-7, 3$\] And $H(1, -2$\]. What Is The Midpoint Of $\overline{GH}$?A. $\left(-3, \frac{1}{2}\right$\] B. $\left(4, \frac{5}{2}\right$\]

Introduction

In geometry, the midpoint of a line segment is the point that divides the segment into two equal parts. It is an essential concept in mathematics, particularly in coordinate geometry. In this article, we will explore the midpoint formula and apply it to find the midpoint of a line segment given its endpoints.

What is the Midpoint Formula?

The midpoint formula is a mathematical concept that allows us to find the midpoint of a line segment given its endpoints. The formula is as follows:

$$\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$$

where $(x_1, y_1)$ and $(x_2, y_2)$ are the coordinates of the endpoints of the line segment.

How to Apply the Midpoint Formula

To apply the midpoint formula, we need to follow these steps:

1. Identify the coordinates of the endpoints of the line segment.
2. Plug the coordinates into the midpoint formula.
3. Simplify the expression to find the midpoint.

Example: Finding the Midpoint of a Line Segment

Let's consider an example to illustrate the application of the midpoint formula. Suppose we have a line segment with endpoints $G(-7, 3)$ and $H(1, -2)$. We want to find the midpoint of this line segment.

Step 1: Identify the Coordinates of the Endpoints

The coordinates of the endpoints are:

• $G(-7, 3)$
• $H(1, -2)$

Step 2: Plug the Coordinates into the Midpoint Formula

Now, we plug the coordinates into the midpoint formula:

$$\left(\frac{-7 + 1}{2}, \frac{3 + (-2)}{2}\right)$$

Step 3: Simplify the Expression

Simplifying the expression, we get:

$$\left(\frac{-6}{2}, \frac{1}{2}\right)$$

$$\left(-3, \frac{1}{2}\right)$$

Therefore, the midpoint of the line segment $\overline{GH}$ is $\left(-3, \frac{1}{2}\right)$.

Conclusion

In this article, we have explored the midpoint formula and applied it to find the midpoint of a line segment given its endpoints. The midpoint formula is a powerful tool in geometry that allows us to find the midpoint of a line segment. By following the steps outlined in this article, you can apply the midpoint formula to find the midpoint of any line segment.

Midpoint Formula: A Summary

• The midpoint formula is: $\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$
• To apply the midpoint formula, identify the coordinates of the endpoints, plug them into the formula, and simplify the expression.
• The midpoint formula is a powerful tool in geometry that allows us to find the midpoint of a line segment.

Frequently Asked Questions

• Q: What is the midpoint formula? A: The midpoint formula is a mathematical concept that allows us to find the midpoint of a line segment given its endpoints.
• Q: How do I apply the midpoint formula? A: To apply the midpoint formula, identify the coordinates of the endpoints, plug them into the formula, and simplify the expression.
• Q: What is the midpoint of a line segment? A: The midpoint of a line segment is the point that divides the segment into two equal parts.

References

• [1] "Midpoint Formula" by Math Open Reference. Retrieved February 27, 2024.
• [2] "Midpoint Formula" by Khan Academy. Retrieved February 27, 2024.

Related Articles

• [1] "Distance Formula: A Comprehensive Guide"
• [2] "Slope Formula: A Comprehensive Guide"
• [3] "Coordinate Geometry: A Comprehensive Guide"
  Midpoint Formula Q&A: Frequently Asked Questions =====================================================

Introduction

In our previous article, we explored the midpoint formula and applied it to find the midpoint of a line segment given its endpoints. However, we understand that there may be some questions and doubts that you may have. In this article, we will address some of the frequently asked questions about the midpoint formula.

Q&A: Midpoint Formula

Q: What is the midpoint formula?

A: The midpoint formula is a mathematical concept that allows us to find the midpoint of a line segment given its endpoints. The formula is as follows:

$$\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$$

where $(x_1, y_1)$ and $(x_2, y_2)$ are the coordinates of the endpoints of the line segment.

Q: How do I apply the midpoint formula?

A: To apply the midpoint formula, you need to follow these steps:

1. Identify the coordinates of the endpoints of the line segment.
2. Plug the coordinates into the midpoint formula.
3. Simplify the expression to find the midpoint.

Q: What is the midpoint of a line segment?

A: The midpoint of a line segment is the point that divides the segment into two equal parts.

Q: Can I use the midpoint formula to find the midpoint of a line segment with negative coordinates?

A: Yes, you can use the midpoint formula to find the midpoint of a line segment with negative coordinates. The formula works for all types of coordinates, including negative coordinates.

Q: Can I use the midpoint formula to find the midpoint of a line segment with decimal coordinates?

A: Yes, you can use the midpoint formula to find the midpoint of a line segment with decimal coordinates. The formula works for all types of coordinates, including decimal coordinates.

Q: How do I know if the midpoint formula is correct?

A: To check if the midpoint formula is correct, you can use the following steps:

1. Plug the coordinates of the endpoints into the midpoint formula.
2. Simplify the expression to find the midpoint.
3. Check if the midpoint is correct by plugging it back into the midpoint formula.

Q: Can I use the midpoint formula to find the midpoint of a line segment with coordinates in different units?

A: Yes, you can use the midpoint formula to find the midpoint of a line segment with coordinates in different units. However, you need to make sure that the units are consistent when you plug the coordinates into the formula.

Q: Can I use the midpoint formula to find the midpoint of a line segment with coordinates in different coordinate systems?

A: Yes, you can use the midpoint formula to find the midpoint of a line segment with coordinates in different coordinate systems. However, you need to make sure that the coordinate systems are consistent when you plug the coordinates into the formula.

Conclusion

In this article, we have addressed some of the frequently asked questions about the midpoint formula. We hope that this article has helped to clarify any doubts that you may have had about the midpoint formula. If you have any further questions, please don't hesitate to ask.

Midpoint Formula: A Summary

• The midpoint formula is: $\left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$
• To apply the midpoint formula, identify the coordinates of the endpoints, plug them into the formula, and simplify the expression.
• The midpoint formula is a powerful tool in geometry that allows us to find the midpoint of a line segment.

Frequently Asked Questions

• Q: What is the midpoint formula? A: The midpoint formula is a mathematical concept that allows us to find the midpoint of a line segment given its endpoints.
• Q: How do I apply the midpoint formula? A: To apply the midpoint formula, identify the coordinates of the endpoints, plug them into the formula, and simplify the expression.
• Q: What is the midpoint of a line segment? A: The midpoint of a line segment is the point that divides the segment into two equal parts.

References

• [1] "Midpoint Formula" by Math Open Reference. Retrieved February 27, 2024.
• [2] "Midpoint Formula" by Khan Academy. Retrieved February 27, 2024.

Related Articles

• [1] "Distance Formula: A Comprehensive Guide"
• [2] "Slope Formula: A Comprehensive Guide"
• [3] "Coordinate Geometry: A Comprehensive Guide"